Resource-constrained turbo-equalization

ABSTRACT

The invention concerns a method for equalizing symbols received from a transmission channel and for decoding data therefrom, the method comprising a sequence of processing steps E i  using an available resource R, each processing step E i  involving a resource cost R i (T ij ) depending upon parameters T ij  relative to an algorithm carried out by said processing step E i , at least a subset of the parameters T ij  being controlled so as to maximise a criterion of performance under the constraint:  
           ∑   i            R   i          (     T   ij     )         ≤   R

[0001] The present invention concerns a method for equalizing symbolsreceived from a transmission channel and decoding data therefrom. Theinvention more specifically concerns an equalization method which isimplemented in a digital signal processor (DSP).

[0002] Equalization is a well known method for removing Inter SymbolInterference (ISI) affecting a transmission channel.

[0003] The signal samples at the channel output can be expressed as:$\begin{matrix}{R_{k} = {{\sum\limits_{i = 0}^{L - 1}{c_{i}D_{k - i}}} + \eta_{k}}} & (1)\end{matrix}$

[0004] where c_(i) are the channel coefficients defining the impulseresponse of the transmission channel (CIR), L is the delay spread of thechannel, D_(k-i) is a M-ary modulated symbol and η_(k) is the sampledadditive white Gaussian (AWG) noise affecting the channel. From equation(1) the transmission channel can be viewed as a finite impulse responsefilter with L taps.

[0005] A first class of equalization methods is concerned withsymbol-by-symbol equalization. A simple equalization method consists inusing a transverse linear filter for cancelling the ISI symbol bysymbol. Of course, the tap coefficients of the transversal filter can beadapted to track the variations of the channel characteristics. Howeverlinear equalization performs poorly due to the effect of noiseenhancement. This effect is mitigated in nonlinear Decision FeedbackEqualization (DFE). A decision feedback equalizer comprises two parts: afeedforward part identical to a transverse linear filter and a feedbackpart including a decision step on the received symbol. The feedback partestimates the ISI contributed by the previously decided symbols andsubtracts this estimation from the transverse linear filter outputbefore the decision on the current symbol is made.

[0006] A second class of equalization methods derives from a MaximumLikelihood Sequence approach called therefore Maximum LikelihoodSequence Estimation (MLSE). According to this approach, the discretememory channel is modelled as a finite-state machine, the internalregister of which having the length of the channel memory. The mostlikely transmitted sequence D_(k), knowing the received sequence R_(k)and the channel coefficients, is obtained by the Viterbi algorithm.Since the number of states of the trellis involved in the Viterbialgorithm grows exponentially with the channel memory length, severalproposals have been made to reduce the number of states to be taken intoaccount. In a first attempt to mitigate this effect, DDFSE (DelayedDecision Feedback Sequence Estimation) combines MLSE and DFE techniquesby truncating the channel memory to a reduced number of terms and byremoving in the branch metrics the tail of the ISI using a decision madeon the surviving sequence at an earlier step (tentative decision). Afurther improvement with respect to error propagation, called RSSE,(Reduced State Sequence Estimation) was inspired by an Ungerboeck-likeset partitioning principle. The RSSE algorithm was originally disclosedin the article of V. M. Eyuboglu et al. entitled “Reduce-state sequenceestimation with set partitioning and decision feedback”, published inIEEE Trans. Commun., Vol. 36, pages 13-20, January 1988. Broadlyspeaking, in RSSE the symbols are partitioned into subsets and Viterbidecoding is performed on a subset-trellis, a node or subset-state of thesubset-trellis being a vector of subset labels instead of a vector ofsymbols like in DDFSE. An advantage of RSSE over DDFSE is that it doesnot use tentative decisions but embeds the uncertainty of the channelresponse within the trellis structure.

[0007] Another possible way of relaxing the constraints in the decodingtrellis is the list-type generalization of the Viterbi algorithm (GVA)proposed by T. Hashimoto in the article entitled “A list-typereduced-constraint generalization of the Viterbi algorithm” published inIEEE Trans. Inform. Theory, vol. IT-33, N^(o)6, November 1987, pages866-876. The Viterbi algorithm is generalized in that, for a given statein the trellis diagram, a predetermined number S of paths (survivors)leading to that state, (instead of a single one in the conventionalViterbi algorithm) are retained for the next step. The retained pathsare then extended by one branch corresponding to the assumed receivedsymbol and the extended paths are submitted to a selection procedureleaving again S survivors per state. The GVA was applied to equalisationby Hashimoto himself in the above mentioned paper and a list-typeViterbi equalizer and later developed by Kubo et al. the articleentitled “A List-output Viterbi equalizer with two kinds of metriccriteria” published in Proc. IEEE International Conference on UniversalPersonnal Comm. ′98, pages 1209-1213.

[0008] Both RSSE and LOVE (List Output Viterbi Equalization) can beregarded as particular cases of Per Survivor Processing (PSP) describedin the article of R. Raheli et al. entitled “Per Survivor Processing”and published in Digital Signal Processing, N^(o)3, July 1993, pages175-187. PSP generally allows joint channel estimation and equalizationby incorporating in the Viterbi algorithm a data aided estimation of thechannel coefficients. This technique is particularly useful in mobiletelecommunication for equalization of fast fading channels.

[0009] Recently, a new method of equalisation has been derived from theseminal principle of turbo-decoding discovered by C. Berrou, A. Glavieux, P. Thitimajshima, and set out in the article entitled “Near Shannonlimit error-correcting coding and decoding: Turbo-coding”, ICC ′93, Vol.2/3, May 1993, pages 1064-1071. This principle has been successfullyapplied to equalization by C. Douillard et al. as described in thearticle entitled “Iterative correction of Intersymbol Interference:Turbo-equalization” published in European Trans. Telecomm., Vol. 6,N^(o) 5, September/October 1995, pages 507-511.

[0010] The basic principle underlying turbo-equalization is that an ISIchannel can be regarded as a convolutional coder and therefore theconcatenation of a coder, an interleaver and the transmission channelitself can be considered as a turbo-coder.

[0011] Turbo-equalization is based on an iterative joint equalizationand channel decoding process. FIG. 1 shows an example of a transmissionsystem using turbo-equalization. The transmitter comprises a systematiccoder (100), e.g. a systematic convolutional coder (K,R) where K isconstraint length and R is the binary rate which encodes the input dataI_(k) into error-control coded data Y_(n) an interleaver (110)outputting interleaved data Y_(n), and a M-ary modulator (120), e.g. aBPSK modulator or a QAM modulator. At the receiver side, theturbo-equalizer TE is represented with dotted lines. The symbols R_(n′)affected by ISI are supplied to a soft equalizer (140) which outputssoft values An representing the reliability of the estimation ofY_(n′. The soft equalization may be implemented by a Soft Output Viterbi Algorithm (SOVA) as described in the article of J. Hagenauer and P. Hoeher entitled “A Viterbi algorithm with soft-decision outputs and its applications” published in Proc. IEEE Globecorn ′)89,pages 47.1.1-47.1.7. Alternately the Maximum A Posteriori (MAP)algorithm initially described in the article of L. Bahl, J. Cocke, F.Jelinek and J. Raviv published in IEEE on Information Theory, vol.IT-20, March 1974, pages 284-287 or a variant thereof (e.g. Log MAP, MaxLog MAP) can be used. The latter algorithms will be generically referredto in the following as APP-type algorithms since they all provide the aposteriori probability for each bit to be decided. For example, thesoft-equalizer of FIG. 1 implements the Log MAP algorithm whichconveniently expresses the reliability information in the form of a LogLikelihood ratio Λ_(n′)=Λ(Y_(n′)). The soft values An are thende-interleaved by the de-interleaver (150) and supplied to a soft outputdecoder which may be again a SOVA decoder or an APP-type decoder. Thesoft decoder uses these soft values and the knowledge of the codingalgorithm to form soft estimates Λ_(k)=Λ(I_(k)) of the initial dataI_(k) which in turn permit to refine the estimation of the receivedsymbols. For that, the latter estimates are passed back to theequalization stage. More precisely, the extrinsic information Ext_(k)produced by the decoding stage, i.e. the contribution of that stage tothe reliability of the estimation, is obtained by subtracting in (191)the soft-output from the soft-input of the decoder. The extrinsicinformation Ext_(k) is then interleaved in interleaver (180) and fedback as a priori information to the soft equalizer (140). The extrinsicinformation derived from a stage must not be included in the soft inputof the same stage. Hence, the extrinsic information Ext_(k) issubtracted in (191) from the output of the soft equalizer. The iterationprocess repeats until the estimation converges or until a time limit isreached. The soft output of the decoder is then compared to a threshold(170) to provide a hard output, i.e. a decision Î_(k) on the bit value.

[0012] The reduced state technique has been successfully transposed tothe MAP algorithm with the view of applying it to turbo-equalization. Inparticular, a List-type MAP equalizer has been described in unpublishedFrench patent applications FR-A-0000207 and FR-A-0002066 filed by theApplicant on Jan. 4, 2000 and Feb. 15, 2000 respectively and includedherein by reference.

[0013] The idea of joint channel estimation and equalization has alsopervaded turbo-equalization. L. Davis, I. Collings and P. Hoeher haveproposed in an article entitled “Joint MAP equalization and channelestimation for frequency-selective fast fading channels” published inProc. IEEE Globecom ′98, pages 53-58 a turboequalizer comprising a MAPequalizer making use of an expanded state trellis. The expansion of thestate trellis beyond the channel memory length introduces additionaldegrees of freedom which are used for estimating the channel parameters.This method is more particularly useful for channels exhibiting fastvarying characteristics for example in case of a transmission channelwith a high velocity mobile terminal.

[0014] Another possible structure of turboequalizer is described in thearticle of A. Glavieux et al. entitled “Turbo-equalization over afrequency selective channel”, International Symposium on Turbo-codes”,Brest, September 1997. In place of the MAP equalizer illustrated in FIG.1, the first stage of the turboequalizer comprises a transversal linearfilter for cancelling ISI from the received symbols in a decisiondirected mode followed by a M-ary to binary soft decoder.

[0015] Although the overall equalization process may be carried out by aplurality of dedicated processing units, a single digital signalprocessor (DSP) is preferred in practice. In such instance, the DSPcarries out the various of steps of equalization per se, deinterleaving,channel and, possibly, source decoding. However, since the processingcapacity of the DSP is limited, the processing time may exceed themaximum delay normally accepted for a telephone transmission. Of course,the choice of a DSP of higher capacity entails additional costs.

[0016] A subsidiary problem arises when the propagation conditions overthe transmission channel vary. It is known from the state of the art toadapt the parameters of the equalizer (e.g. adaptive filter withvariable number of taps) or to modify the decoder (in concertation withthe encoder) e.g. by changing the puncturing rate in a channelencoder/decoder or changing the compression algorithm in a sourceencoder/decoder. This change may cause a temporary overrun of theprocessing capacity of the DSP. On the other hand, the choice of anoversized DSP which complies with the “worst-case” requirements iseconomically expensive and technically unsatisfactory.

[0017] The object of the present invention is to propose a method (and acorresponding device) for equalizing symbols received from atransmission channel and decoding data therefrom which solves the aboveaddressed problems.

[0018] These problems are solved by carrying out the method steps (resp.by implementing the technical features) recited in the characterisingpart of claim 1 (resp. claim 23)

[0019] The invention will be better understood from a description of thevarious embodiments of the invention in relation to the followingfigures.

[0020]FIG. 1 schematically shows a known transmission system comprisinga turbo-equalizer,

[0021]FIG. 2 schematically shows the structure of a receiver accordingto the invention,;

[0022]FIG. 3 schematically shows the structure of a transmitteraccording to the invention;

[0023] The basic idea underlying the invention is to optimize theoverall performance of a DSP-based receiver under a constraint on anavailable resource. This resource may be, for example a processing time,a number of operations, the size of a memory, the complexity of acircuit, etc. In the following, we assume that the DSP is in charge ofequalization, channel decoding and possibly source decoding. Dependingon the case, the criterion of performance will be a bit-error rate, ablock-error rate, a distortion measure, a quality of service (QoS), atransmission capacity etc.

[0024] It is assumed that the various processing steps E_(i) involved inequalization, channel and possibly source decoding are based onalgorithms depending upon a set of parameters T_(ij), at least a subsetof which are controllable by the DSP. More concretely, some parametersof the system are fixed (e.g. the size of a modulation alphabet) andothers (e.g. the number of states of a trellis) can be modified by theDSP. If each step E_(i) entails a resource cost R_(i)(T_(ij)) whereT_(ij) are the above mentioned algorithm parameters, the methodaccording to the invention proposes to maximize the criterion ofperformance while the resource constraint is met:${\sum\limits_{i}{R_{i}\left( T_{ij} \right)}} \leq R$

[0025] where the R is the available resource. In other words, thedifferent process steps share the common resource R so as to maximisethe above mentioned criterion of performance.

[0026] The method according to the invention will be illustrated with anexample directed to resource-constrained turbo-equalization , althoughthe invention is obviously not limited thereto. FIG. 2 shows aturbo-equalizer implementing the method according to the invention anddescribed hereafter.

[0027] The turbo-equalizer comprises a soft-equalizer (240) of the APPtype, preferably a Log MAP equalizer The number of states in the APPtrellis is equal to M^(L-1) where M is size of the modulation alphabetand L is the delay spread of the transmission, i.e. the constraintlength of the channel expressed in a number of samples (in other wordsthe size of the channel memory is equal to L-1 samples). For a largememory length however, a second configuration using a reduced statetechnique is preferred. The number of states taken into account is thenreduced to M^(J-1) by truncating the constraint length to a strictlypositive integer, J<L (i.e. the channel memory is truncated to J-1). Forexample, a List-type APP equalizer as disclosed in the above mentionedpatent applications may be used in such instance. In contrast, anexpanded state trellis may be opted for in case of fast varyingcharacteristics of the transmission channel. The higher number of statesin the trellis , M^(J-1) where J>L enables a joint estimation of thechannel coefficients and of the data, as explained in the article of L.Davis mentioned above.

[0028] In general, the value of J will be set greater or lower than Laccording to the propagation conditions, e.g. the shape and thevariation of the channel impulse response. For example, if thepropagation over a mobile transmission channel involves a Line of Sight(LOS) component, in other words if the channel is affected by Riceandispersion, a reduced state trellis (J<L) could be used. On the otherhand, if the transmission channel suffers from fast-fading because thevelocity of the mobile terminal is high an expanded state trellis (J>L)could be chosen.

[0029] The soft equalizer is followed by a deinterleaver (250) and asoft-decoder (260).

[0030] According to a first embodiment, the value of the constraintlength K of the code is made variable. The soft decoder (260) (as wellas the associated coder at the transmitter side) is adaptive so as tooperate with different values of K and hence different trellis sizes.More specifically, the value of K is increased when L (and moregenerally J) decreases and is decreased when L (or J) increases. It hasbeen discovered indeed that turbo-equalization performs less efficientlywhen the delay spread of the transmission channel is small. Morespecifically, for the same number of iterations, the BER gain achievedby the iterative process (also called “turbo-effect”) is lower for asmall delay spread than for a large delay spread. This can be explainedby the fact that the delay spread of transmission channel can beregarded as equivalent to the constraint length of a code and thatturbo-equalization is less efficient for small constraint lengths. Theinvention proposes to compensate for a small delay spread of thetransmission channel by increasing the constraint length at the codingstage. According to the invention the choice of K is made so as to meeta resource constraint, for example a complexity constraint. The overallcomplexity of the of the turbo-equalizer can be expressed as:

[0031] C_(turbo.)=C_(equalizer)+C_(deinterleaver)+C_(decoder) whereC_(equalizer), C_(deinterleaver), C_(decoder) account for the respectivecomplexities of the equalizer, the deinterleaver and the decoder. Thecomplexity of the deinterleaver is constant i.e. does not depend on K orJ. The complexity of the MAP decoder is proportional to the number ofstates involved in the trellis i.e. can be expressed as a. 2^(K-)1 wherea is a fixed coefficient. Similarly, the complexity of thesoft-equalizer can be expressed as b.M^(J-1) if it is a MAP equalizer oras b′. L , where b,b′ are fixed coefficients, if it is based on atransversal linear filter with L taps. The complexity constraint cantherefore be written as:

[0032] a.2^(K-1)+b.M^(J-1)<C_(max) (2) when soft equalizer (221) is aMAP equalizer and

[0033] a.2^(K-1)+b′.L<C_(max) (3) when the soft equalizer (221) is basedon a transversal linear filter.

[0034] The value of the parameter K is chosen to optimize the BER underthe constraint (2) or (3). Preferably, for a given J or L, K is chosenas the highest possible integer meeting the constraint.

[0035] When the receiver decides to modify K, it sends a request forincrementing or decrementing K to the transmitter over a reversechannel. This can be done by sending a control bit over a dedicatedphysical control channel (DPCCH) if the system is a mobiletelecommunication system.

[0036] According to a second embodiment, the size M of the modulationalphabet is made variable and the constraint length is kept constant .The MAP equalizer (240) (as well as the associated modulator at thetransmitter side) is adaptive so as to operate with different values ofM and hence different trellis sizes. More specifically, the value of Mand, hence, the capacity of the transmission channel is increased when L(and more generally J) decreases and is decreased when L (or J)increases. M is chosen so as meet the constraint (2). The modulation cantypically range between 2-QAM or BPSK to 64-QAM. However, since the BERincreases with the modulation level, the available received power shouldbe high enough to allow switching to a higher modulation level.

[0037] According to a third embodiment, the number N of iterations ofthe turbo-equalization process is made variable. The BER gain achievedby turbo-equalization increases with the number N of iterations. It maybe therefore desirable to increase N while the constraint on theavailable resource, for example the processing power of the DSP, isstill met. In general, the amount of processing power required byturbo-equalization increases linearly versus N (in some instances,however, the DSP may benefit from parallel computation and the increaseversus N may be less than linear) and the constraints (2) and (3) haveto be replaced by (2′) and (3′) respectively:

[0038] N.(a.2^(K-1)+b.M^(J-1))<C_(max) (2′)

[0039] N.(a.2^(K-1)+b′.L)<C_(max) (3′)

[0040] In general, the parameters M,J,K,N of the turbo-equalizer arevariable and chosen so as to meet a criterion of performance (BER,capacity) under the complexity constraint given by (2) or (3) (oralternately (2′),(3′)). More generally, if the system comprises a sourcedecoder after the channel decoder, a further parameter for varying thecompression ratio may be taken into account. In any case, the receiverhas to send to the transmitter a request for modifying one or aplurality of the parameters M,J,K etc. This could be done by sending acontrol word whose bits thereof indicate whether to increase or decreasethe corresponding parameters.

[0041]FIG. 3 schematically shows the structure of a transmitter for usewith the receiver of FIG. 2. The transmitter comprises a systematiccoder (300) e.g. a systematic convolutional coder whose constraintlength is variable, an interleaver (310) and a M-ary modulator (330).Furthermore, the transmitter comprises a controller (330) which receivesthe requests for incrementing or decrementing the parameters, here M andK from the receiver. The controller updates the different parameters andsupplies the updated value K to the coder and the updated value M to themodulator. In addition, the receiver may also include a source coderbefore the channel coder (300) which similarly could be controlled bythe controller (330).

[0042] In addition, the controller (330) may control the transmissionpower of the transmitter. Indeed, a modification of the parametersM,J,K,N may result in a decrease of the BER. Hence, it is possible tolower the signal to noise ratio at the receiving side while keeping anacceptable target BER level. This measure is particularly prescribed forlowering the interference level in a cellular telecommunication system.

1. Method for equalizing symbols received from a transmission channeland for decoding data therefrom, the method comprising a sequence ofprocessing steps E_(i) using an available resource R, each processingstep E_(i) involving a resource cost R_(i)(T_(ij)) depending uponparameters T_(ij) relative to an algorithm carried out by saidprocessing step E_(i), characterised in that at least a subset of theparameters T_(ij) are controlled so as to maximise a criterion ofperformance under the constraint:${\sum\limits_{i}{R_{i}\left( T_{ij} \right)}} \leq R$


2. Method as claimed in claim 1, characterised in that said subset ofparameters T_(ij) are dynamically adapted when a transmission conditionvaries.
 3. Method as claimed in claim 1 or 2, characterised in that theprocessing steps includes the iteration of a soft equalizing step forequalizing symbols received from a transmission channel, ade-interleaving step and a soft decoding step.
 4. Method as claimed inclaim 3, characterised in that the soft equalizing step is performedaccording to an APP type algorithm involving a number of states M^(J-1)where M is the alphabet size of the modulation used over thetransmission channel, J is a strictly positive integer and the softdecoding step is performed according to an APP type algorithm involvinga number of states 2^(K-1) where K is constraint length of aconvolutional code used for coding said data.
 5. Method as claimed inclaim 4, characterised in that the soft equalizing step is performedaccording to a List-type APP algorithm.
 6. Method as claimed claims 4 or5, characterised in that J is chosen equal to the delay spread L of thetransmission channel and that at least one of K and M is controlled sothat a.2^(K-1)+b.M^(L-1) is lower than a predetermined resource value,where a and b are fixed coefficients.
 7. Method as claimed in claims 4or 5, characterised in that J is chosen lower or greater than the delayspread L of the transmission channel according to a propagationcondition over the transmission channel.
 8. Method as claimed in claim7, characterised in that the propagation condition is a Line of Sight orNon Line of Sight condition.
 9. Method as claimed in claim 7,characterised in that the propagation condition is a fast fading or slowfading condition.
 10. Method as claimed in claims 7, 8 or 9,characterised in that at least one of K, M and J is adapted so thata.2^(K-1)+b.M^(J-1), where a and b are fixed coefficients, is lower thana predetermined resource value.
 11. Method as claimed in claim 7, 8 or9, characterised in that at least one of K,M,J,N is adapted so thatN.(a.2^(K-1)+b.M^(J-1)), where a and b are fixed coefficients and N isthe number of iterations, is lower than a predetermined resource value.12. Method as claimed in any of claims 6 to 11, characterised in that Kis increased when J is decreased and K is decreased when J is increased13. Method as claimed in any claims 6 to 11, characterised in that M isincreased when J is decreased and M is decreased when J is increased.14. Method as claimed in claim 5, characterised in that the softequalizing step comprises a filtering step for cancelling theintersymbol interference over the transmission channel, the filterhaving L taps where L is the delay spread of the transmission channel.15. Method as claimed in claim 14, characterised in that the softdecoding step is performed according to an APP type algorithm involvinga number of states 2^(K-1) where K is adapted so that a.2^(K-1)+b′.L,where a and b′ are fixed coefficients, is lower than a predeterminedresource value.
 16. Method as claimed in claim 14, characterised in thatthe soft decoding step is performed according to an APP type algorithminvolving a number of states 2^(K-1) where at least one of K and N isadapted so that N.(a.2^(K-1)+b′.L), where a and b′ are fixedcoefficients, is lower than a predetermined resource value.
 17. Methodas claimed in claim 15 or 16, characterised in that K is increased whenL decreases and is decreased when L increases.
 18. Method as claimed inclaims 3, 4 or 5, characterised in that the number of iterations isadjusted so that said constraint is met.
 19. Method as claimed in any ofthe preceding claims, characterised in that the resource R is a timeinterval.
 20. Method as claimed in any of the claims 1 to 18,characterised in that the resource R is the size of a memory.
 21. Methodas claimed in any of the claims 1 to 18, characterised in that theresource R is the processing power of a processor.
 22. Method as claimedin any of the preceding claims, characterised in that the criterion ofperformance is a function of the error rate.
 23. Receiver comprisingmeans for carrying a method according to any of the preceding claims.24. Method for coding data and modulating said coded data comprising aconvolutional coding step, an interleaver interleaving said coded data,a modulator for modulating the interleaved data into M-ary symbols to betransmitted to a receiver, the constraint length of the convolutionalcode being varied upon a request of a receiver.
 25. Method as claimed inclaim 24, characterised in that the size M of the modulation alphabet isvaried upon a request of the receiver.
 26. Transmitter comprising meansfor carrying out a method according to claim 24 or
 25. 27.Telecommunication system comprising a receiver according to claim 20 anda transmitter according to claim 26.